Finite Group Databasebeta

← #18085800

Subgroups — #18085800

Order 4864.

526 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 75 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14571899C211yesmaximal, characteristic
2#14563709C211yesmaximal, characteristic
3#14563709C211yesmaximal, characteristic
4C19⋊#1304C211yesmaximal, characteristic
5C19⋊#1304C211yesmaximal, characteristic
6C19⋊#1304C211yesmaximal, characteristic
7C19×#1819C211yesmaximal, characteristic
8#11926480—22no—
9#11926467—22no—
10#11926467—22no—
11#11926400C2211yescharacteristic
12#11926400C2211yescharacteristic
13#11926400C2211yescharacteristic
14#11926400C2211yescharacteristic
15#11926311—22no—
16#11926311—22no—
17C22×C22⋊C4×C19C2211yescharacteristic
18C19×#379C2211yescharacteristic
19C19×#379C2211yescharacteristic
20C19×#342—22no—
21C25×C19C2311yescharacteristic
22C23×C4×C19Q811yescharacteristic
23C23×C4×C19Q811yescharacteristic
24C2×C22⋊C4×C19—21no—
25C2×C22⋊C4×C19—21no—
26C2×C22⋊C4×C19—21no—
27C2×C22⋊C4×C19—21no—
28C2×C22⋊C4×C19—21no—
29C2×C22⋊C4×C19—21no—
30C2×C22⋊C4×C19—21no—
31C2×C22⋊C4×C19—21no—
32C2×C22⋊C4×C19—21no—
33C2×C22⋊C4×C19—21no—
34C2×C22⋊C4×C19—21no—
35C2×C22⋊C4×C19D412yes—
36C2×C22⋊Dic19—21no—
37C2×C22⋊Dic19—21no—
38C2×C22⋊Dic19—21no—
39C2×C22⋊Dic19—21no—
40C2×C22⋊Dic19—21no—
41C2×C22⋊Dic19—21no—
42C2×C22⋊Dic19—21no—
43C2×C22⋊Dic19—21no—
44C2×C22⋊Dic19—21no—
45C2×C22⋊Dic19—21no—
46C2×C22⋊Dic19D412yes—
47C2×C22⋊Dic19D412yes—
48C2×C4⋊Dic19—22no—
49C2×Dic19⋊C4—22no—
50C2×Dic19⋊C4—22no—
51C19⋊#95—22no—
52C24×C19—42no—
53C24×C19—81no—
54C24×C19—81no—
55C24×C19C2×D411yescharacteristic
56C24×C19C2×D411yescharacteristic
57C24×C19C2×D411yescharacteristic
58C24×C19C2×Q811yescharacteristic
59C24×C19#4111yescharacteristic
60C24×C19#4111yescharacteristic
61C24×C19#4111yescharacteristic
62C22×C4×C19—22no—
63C22×C4×C19—21no—
64C22×C4×C19—21no—
65C22×C4×C19—21no—
66C22×C4×C19—21no—
67C22×C4×C19—21no—
68C22×C4×C19—21no—
69C22×C4×C19—41no—
70C22×C4×C19—81no—
71C22×C4×C19—81no—
72C22×Dic19—22no—
73C22×Dic19—22no—
74C22×Dic19—41no—
75C22×Dic19—41no—
76C22⋊C4×C19—41no—
77C22⋊C4×C19—41no—
78C22⋊C4×C19—41no—
79C22⋊C4×C19—41no—
80C22⋊C4×C19—42no—
81C22⋊C4×C19—42no—
82C22⋊C4×C19—81no—
83C22⋊C4×C19—81no—
84C22⋊C4×C19—81no—
85C22⋊C4×C19—81no—
86C22⋊Dic19—42no—
87C22⋊Dic19—42no—
88C22⋊Dic19—42no—
89C22⋊Dic19—42no—
90C22⋊Dic19—81no—
91C22⋊Dic19—81no—
92C22⋊Dic19—81no—
93C22⋊Dic19—81no—
94C22⋊Dic19—81no—
95C22⋊Dic19—81no—
96C22⋊Dic19—81no—
97C22⋊Dic19—81no—
98C4⋊Dic19—82no—
99Dic19⋊C4—82no—
100Dic19⋊C4—82no—
101#10393—191nomaximal, Sylow
102C23×C19—22no—
103C23×C19—22no—
104C23×C19—22no—
105C23×C19—41no—
106C23×C19—41no—
107C23×C19—41no—
108C23×C19—41no—
109C23×C19—41no—
110C23×C19—41no—
111C23×C19—41no—
112C23×C19—41no—
113C23×C19—41no—
114C23×C19—41no—
115C23×C19—41no—
116C23×C19—41no—
117C23×C19—41no—
118C23×C19—41no—
119C23×C19—41no—
120C23×C19—41no—
121C23×C19—41no—
122C23×C19—41no—
123C23×C19—88no—
124C23×C19#12011yescharacteristic
125C23×C19C22⋊Q811yescharacteristic
126C23×C19C22⋊Q811yescharacteristic
127C23×C19C22⋊Q811yescharacteristic
128C23×C19#12411yescharacteristic
129C23×C19#12411yescharacteristic
130C23×C19#12411yescharacteristic
131C2×C4×C19—42no—
132C2×C4×C19—42no—
133C2×C4×C19—41no—
134C2×C4×C19—41no—
135C2×C4×C19—42no—
136C2×C4×C19—81no—
137C2×C4×C19—81no—
138C2×C4×C19—81no—
139C2×C4×C19—81no—
140C2×C4×C19—81no—
141C2×C4×C19—81no—
142C2×C4×C19—81no—
143C2×C4×C19—81no—
144C2×C4×C19—81no—
145C2×Dic19—42no—
146C2×Dic19—42no—
147C2×Dic19—42no—
148C2×Dic19—42no—
149C2×Dic19—42no—
150C2×Dic19—42no—
151C2×Dic19—81no—
152C2×Dic19—81no—
153C2×Dic19—81no—
154C2×Dic19—81no—
155C2×Dic19—81no—
156C2×Dic19—81no—
157#2842—191no—
158#1819—191no—
159#1819—191no—
160#1819D1911yescharacteristic
161#1304—191no—
162#1304—191no—
163#1304—191no—
164C22×C19—21no—
165C22×C19—21no—
166C22×C19—21no—
167C22×C19—21no—
168C22×C19—21no—
169C22×C19—21no—
170C22×C19—21no—
171C22×C19—21no—
172C22×C19—21no—
173C22×C19—21no—
174C22×C19—21no—
175C22×C19—21no—
176C22×C19—21no—
177C22×C19—21no—
178C22×C19—21no—
179C22×C19—21no—
180C22×C19—21no—
181C22×C19—21no—
182C22×C19—21no—
183C22×C19—21no—
184C22×C19—44no—
185C22×C19—82no—
186C22×C19—82no—
187C22×C19—82no—
188C22×C19—82no—
189C22×C19—82no—
190C22×C19—82no—
191C22×C19#39311yescharacteristic
192C22×C19#45812yes—
193C4×C19—82no—
194C4×C19—81no—
195C4×C19—81no—
196C4×C19—161no—
197Dic19—82no—
198Dic19—82no—
199Dic19—161no—
200Dic19—161no—
201C22×C22⋊C4C2×D1911yescharacteristic
202#399—382no—
203#396—382no—
204#396—382no—
205#379—191no—
206#379—191no—
207#379—191no—
208#379—191no—
209#379C2×D1911yescharacteristic
210#379C2×D1911yescharacteristic
211#342—22no—
212#342—382no—
213#342—382no—
214C2×C19—22no—
215C2×C19—41no—
216C2×C19—41no—
217C2×C19—41no—
218C2×C19—41no—
219C2×C19—41no—
220C2×C19—41no—
221C2×C19#203011yescharacteristic
222C2×C19#203211yescharacteristic
223C2×C19#203211yescharacteristic
224C25C22×D1911yescharacteristic
225C23×C4Dic3811yescharacteristic
226C23×C4Dic3811yescharacteristic
227C2×C4⋊C4—382no—
228C2×C4⋊C4—382no—
229C2×C4⋊C4—382no—
230C2×C22⋊C4—21no—
231C2×C22⋊C4—21no—
232C2×C22⋊C4—21no—
233C2×C22⋊C4—21no—
234C2×C22⋊C4—21no—
235C2×C22⋊C4—21no—
236C2×C22⋊C4—21no—
237C2×C22⋊C4—21no—
238C2×C22⋊C4—21no—
239C2×C22⋊C4—21no—
240C2×C22⋊C4—21no—
241C2×C22⋊C4—192no—
242C2×C22⋊C4—192no—
243C2×C22⋊C4—381no—
244C2×C22⋊C4—381no—
245C2×C22⋊C4—381no—
246C2×C22⋊C4—381no—
247C2×C22⋊C4—381no—
248C2×C22⋊C4—381no—
249C2×C22⋊C4—381no—
250C2×C22⋊C4—381no—
251C2×C22⋊C4—381no—
252C2×C22⋊C4—381no—
253C2×C22⋊C4C22⋊D1912yes—
254#95—382no—
255C19#1039311yescharacteristic, complemented, Sylow
256C24—42no—
257C24—81no—
258C24—81no—
259C24C2×Dic3811yescharacteristic
260C24#6454111yescharacteristic
261C24D4×D1911yescharacteristic
262C24D4×D1911yescharacteristic
263C24#6454311yescharacteristic
264C24#6454311yescharacteristic
265C24C2×C22⋊D1911yescharacteristic
266C22×C4—22no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—41no—
274C22×C4—81no—
275C22×C4—81no—
276C22×C4—382no—
277C22×C4—382no—
278C22×C4—761no—
279C22×C4—761no—
280C4⋊C4—1522no—
281C4⋊C4—1522no—
282C4⋊C4—1522no—
283C22⋊C4—41no—
284C22⋊C4—41no—
285C22⋊C4—41no—
286C22⋊C4—41no—
287C22⋊C4—42no—
288C22⋊C4—42no—
289C22⋊C4—81no—
290C22⋊C4—81no—
291C22⋊C4—81no—
292C22⋊C4—81no—
293C22⋊C4—762no—
294C22⋊C4—762no—
295C22⋊C4—762no—
296C22⋊C4—762no—
297C22⋊C4—1521no—
298C22⋊C4—1521no—
299C22⋊C4—1521no—
300C22⋊C4—1521no—
301C22⋊C4—1521no—
302C22⋊C4—1521no—
303C22⋊C4—1521no—
304C22⋊C4—1521no—
305C23—22no—
306C23—22no—
307C23—22no—
308C23—41no—
309C23—41no—
310C23—41no—
311C23—41no—
312C23—41no—
313C23—41no—
314C23—41no—
315C23—41no—
316C23—41no—
317C23—41no—
318C23—41no—
319C23—41no—
320C23—41no—
321C23—41no—
322C23—41no—
323C23—41no—
324C23—41no—
325C23—41no—
326C23—88no—
327C23#1059732411yescharacteristic
328C23#1059732411yescharacteristic
329C23#1059733111yescharacteristic
330C23#1059733111yescharacteristic
331C23#1059737011yescharacteristic
332C23#1059738211yescharacteristic
333C23#1059738311yescharacteristic
334C2×C4—42no—
335C2×C4—42no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—42no—
339C2×C4—81no—
340C2×C4—81no—
341C2×C4—81no—
342C2×C4—81no—
343C2×C4—81no—
344C2×C4—81no—
345C2×C4—81no—
346C2×C4—81no—
347C2×C4—81no—
348C2×C4—762no—
349C2×C4—762no—
350C2×C4—762no—
351C2×C4—762no—
352C2×C4—762no—
353C2×C4—762no—
354C2×C4—1521no—
355C2×C4—1521no—
356C2×C4—1521no—
357C2×C4—1521no—
358C2×C4—1521no—
359C2×C4—1521no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—21no—
380C22—44no—
381C22—82no—
382C22—82no—
383C22—82no—
384C22—82no—
385C22—82no—
386C22—82no—
387C22#1192645611yescharacteristic
388C22#1192673312yes—
389C4—82no—
390C4—81no—
391C4—81no—
392C4—161no—
393C4—3041no—
394C4—3041no—
395C4—1522no—
396C4—1522no—
397C2—22no—
398C2—41no—
399C2—41no—
400C2—41no—
401C2—41no—
402C2—41no—
403C2—41no—
404C2#1456480211yescharacteristic
405C2#1456481211yescharacteristic
406C2#1456481211yescharacteristic
subgroupG/H
centerC22#11926456
commutator, prime radical, cosocleC25×C19C23
FrattiniC25C22×D19
FittingC19×#1819C2
socleC22×C19#393
hypercenter#1819D19
hypocenterC19#10393
LCSG ▷ C25×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C25 ◁ #1819

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
255. C19#10393semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#145718992
#145637092
C19⋊#13042
C19×#18192
#1039319